Trimaran crossbeam calculations

This is an ask for help, please. I also posted this in the very helpful thread on cat beams but got no replies so thought a new thread might be a good idea.

So here is my problem. What is the worst case scenario on which to design the beams for a trimaran? Okay, yes, the worst is an horrible co-incidence of barely measurable, not really calculable forces and factors - but what is sane and reasonable?

Rob James ( who co-designed the Colt Cars GB tri with Ron Holland) says in his book 'Multihulls Offshore' that the largest static load = half beam x full weight of boat. Okay, that's straightforward and easily understandable - she's heeled over to the point of maximum righting moment, the main hull is just coming out, full vessel weight on one float. In this static situation, though James doesn't say so, the weight is obviously taken by, say the two crossbeams on the port side if she's heeled to port.

Then he says, to address the dynamic loads :

"For instance, if the trimaran takes off over a wave, drops 10ft, lands only on her floats with the main hull over a trough and comes to rest after sinking two feet into the water, the resulting calculations show a beam strength required that is similar to the static tests just done." ( I'd like to see the paper work on those calculations.)
James doesn't say, and it's not obvious, if the load should be considered as taken on one beam or two.

So, the 10 ft plunge results in momentary very high loads on both beams on the port side? On the port and starboard aft beam pair? On the starboard fwd beam??? What would you engineer a design for?

My design is for a 38' light cruiser, absolute maximum overload displacement 7265 lbs, normal design displ. 6100 lbs. The usual crossbeam layout, that is two beams per side, one fwd one aft. I want to use round ali 6061 tubes for building space, transport to water and very occasional de-mount reasons. Using Beam Boy to do the number crunching I get fairly good results using 12" tube, 1/4" wall (304.8mm x 6.35mm). I'm aiming to have max bending stress less than the fatique stress of 96.5 MPa, and acceptable deflection, though this is coming out a little high at 2 to 5 %. There are no rigging loads on the beams. The weights, approx 500lb for 4 tubes seem okay.

Is it over the top to take as worst case / max possible load the case of one beam takes it all? That is, one beam loaded by total vessel displacement? And in this case is the fatique stress criterion relevant? Is it acceptable to view this as a one-off 'it's okay if it doesn't break' calculation?

Or is it more rational to accept the case of one beam loaded by half the total vessel displacement?

"For instance, if the trimaran takes off over a wave, drops 10ft, lands only on her floats with the main hull over a trough and comes to rest after sinking two feet into the water, the resulting calculations show a beam strength required that is similar to the static tests just done."

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This clearly implies the two "floats" are supporting the main hull.

For a dynamic case, you should perform this calculation at 2g, not static 1g, as a minimum. But this also depends upon the sea states you expect to encounter.

As for fatigue, that depends upon, as noted, the sea states, hence the frequency of encounter, and then the material of your choice (what is the fatigue limit), and the structural joints and load paths, and finally the skill of the laminator coupled with the QA s/he performs during construction.....just for starters.

Rob James was a colleague of Chay Blyth and so knew the design of GB3 and GB4. These boats were stressed out by the Wolfson Unit so I'd believe the figures he came up with for the design of Colt Cars.

You don't say how wide your boat is, or whether it has hull wings. The beam lever is a very important factor and the shorter you can make it the better

I agree with Adhoc, you need to work on 2g (but in a way that is just a safety factor)

It sounds like your boat might be similar to Paradox, so worth checking with Dazcats what they used. To me a 12in OD beam sounds large. I'd avoid using a round tube if at all possible. its not an efficient beam and it can twist in the mountings, whereas an oval beam is stiffer and cannot twist

BUT...2g / 1g/ xg ? !0ft drop, 12 ft drop, 16 ft drop and on. James says the dynamic load can be considered similar to the load in the maximum static case. So in that sense it seems that's sufficient assessment of the load.

But still, should you engineer one beam ( and by one beam I mean for instance the port forward beam on it's own not the port and starboard forward beams together) to take the full displacement / maximum static righting moment? In other words it's the difference between a load of 3300 kg (total max displacement) or a load of 1650 kg for each beam if two beams take the load.

Oval beam sounds interesting. I shall look at that and see how that works out. Yes, the design does have wings and the unsupported beam length and lever is one of the main reasons I put my question to start with. The maximum design load on the tubes / beams has a direct effect on the maximum possible Beam Over All I can achieve within the eternal circle of design compromises. At the moment I'm designing around 24' max beam, but would like to go a little wider if I can. With floats 3' wide and the main hull wings, I have beam/ tube unsupported lengths of around 4.5' so set it up in BeamBoy as a cantilever supported beam 7.5 ft long with a point load at 4.5 ft from the support, as if the load is delivered at the inner sheer line of the float.

BUT...2g / 1g/ xg ? !0ft drop, 12 ft drop, 16 ft drop and on. James says the dynamic load can be considered similar to the load in the maximum static case. So in that sense it seems that's sufficient assessment of the load.

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You’re asking for advice. Yet you seem to wish to stick with what you’ve read from Rob James.
Either you’re happy with his solutions, or you’re not. No point me or Richard, or anyone else advising you if you’ve already made up your mind, neh? Doesn’t bother me either way, but YOU need to decide which way to go, then stick to it and design accordingly.

But still, should you engineer one beam ( and by one beam I mean for instance the port forward beam on it's own not the port and starboard forward beams together) to take the full displacement / maximum static righting moment? In other words it's the difference between a load of 3300 kg (total max displacement) or a load of 1650 kg for each beam if two beams take the load.

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Hence not sure what you’re asking? His (RJ’s) statement is clear how the loads are applied using his method.

The maximum design load on the tubes / beams has a direct effect on the maximum possible Beam Over All I can achieve within the eternal circle of design compromises.

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Not necessarily, since one of the main drivers in determining the load is the displacement, not just the beam. It is all about levers and hence total moments. Therefore, if you’re able to design a light weight boat, then the total moment, for your given beam, reduces.

The design of the amas has a huge importance in the scenario you propose. A narrow vee hull will sink more freely than a flatter or rounded bottom one. That will influence the acceleration forces. Also, considering two amas of equal flotation, a round bottomed one will have less leverage (being less tall) than a deep vee design. Another important point to consider, is that the likelihood of the boat falling completely flat is almost nil. Most likely it will slide sideways on waves and have slamming loads on the sides of the amas.

Jamez - thanks for that link to the Kurt Hughes 38 Very nice piece of work and is very close to what I'm trying to do, though different in style / character of boat and some general arrangement detail - I'm going with a centre cockpit / Searunner type layout.

Gonzo, thanks for your reply. I agree with you about the many, many different loads, accelerations, angles from which loads will come in reality out on the sea and the complex reactions of the tri and her parts to them. Are they measurable and calculable? Or do we have to take approximations? I guess that's why Rob James experience is attractive. I have no way of estimating or accurately calculating the real forces so look to precedent and previous experience. Your point about the boat falling flat being unlikely is spot on I think and illustrates the gap so frequently, frustratingly found between an example in a book and WHAT REALLY HAPPENS.

Ad Hoc, you're right Beam Boy is a freely available program that takes a lot of the tedium out of calculating 2nd moments of area, bending moment, bending stress and deflection. Like many digital ways of doing things it gives such fast results it's easy to look at small or large changes in the load, the length of the beam/ lever and the size, structure and type of material used in the beam. Try it, you might like it, a lot of people find it very useful.

Langdon,
From the mathematical point of view, I can concieve how Ad Hoc's and Richard Woods' advice (2g loads) is in line with the citation you've taken from Rob James' book:

"For instance, if the trimaran takes off over a wave, drops 10ft, lands only on her floats with the main hull over a trough and comes to rest after sinking two feet into the water, the resulting calculations show a beam strength required that is similar to the static tests just done."​

If the citation is typed correctly, James is talking about "floats" in this case, not "the float". So he considers a situation where the boat has just fallen in water with the two amas plunging into two adjacent wave's crests (or a crest and a half-crest of the next wave) and the main hull suspended over the wave trough.

In this case the load is divided between two amas and it's designers' task to establish how much of it will compete to the port and how much to the starboard ama. If you decide that it's 50-50, and then apply to this load a safety factor of 2 (which is 2g), you get a number similar to the static case - each ama has to carry a load comparable to the whole boats' weight. In this way the author probably neglects the load relief due to inertial forces (the so-called "inertial relief"), which is favorable to the safety.

In any case - be it "2g" or "the whole weight on one ama" - it remains a matter of choice and experience, more or less supported by some real-life measured data. I have done some FEM calculations for ship structures with loadcases involving up to 4.5 g accelerations in a seaway (required by the SOR), for example. The load factors will depend on the ship and mission type and, of course, on the failure track-record of similar designs.

As about sideways loads mentioned by gonzo - they will reduce the total bending moment but will introduce an axial compression to the cross beam. So, while it plays in favor of safety to ignore this term when scantling for bending moment, it would imho be wise to check for eventual slender-beam buckling instability (if it actually is slender). The simple-to-use Euler's formula can give you a first approximation to how far away you are from the danger zone.

A final note - give a due consideration to the material fatigue, as Ad Hoc pointed out. It is particularily important for aluminum beams, as this material is not a good performer when it comes to cyclic loads, which can reduce the maximum permissible (or allowable) stress down to just 20% of the maximum static yield stress in some cases.

I also went through this process some 15 years ago. I was designing a 40ft cruising tri - half Searunner half modern flared main hull. Had boards in the amas. I was a tri tragic - had a Nugget and then Twiggy. Have everything written tris. Still have Piver's three books proudly on my shelf (They took some getting) After drawing the boat for about 18 months a few doubts crept into my mind.

EVERYONE was telling me I was stupid to build a tri. The bloke I worked for voluntarily for three months (to learn strip plank) said they cost more and sold cheaper, my friend who loves Newicks, a guy with a lovely wishbone cat all had said we would get more boat with a cat.

So one night instead of playing with the tri I drew a cat. It had twice the room of the tri straight off. In the end we built a cat and I have never regretted it. So my first bit of advice is - Can you get what you want in a cat - it will be cheaper, faster to build and better resale.

If not (it took me years to be worn down) then why not get your trusty tape measure and reverse engineer some alloy beam tris. Ones like Kelsall's Trifle, The Explorer 34 by White, you can even use Farrier's alloy beam arms in tension and work out max possible load in them. Let's face it - most designers of previous boats didn't know lots about dynamic loads. They used safe materials and checked if they looked like breaking and beefed them up. And the boats have proven themselves. Start with as many tris as you can as a reverse engineering base. I did them same thing with a few cats when I couldn't get a handle on cat beams. It helped me work out fact from fiction.

Just remembered that there is an entire chapter on converting a 35ft Kelsall tri from alloy beams to glass ones. The book is called "The Atlantic challenge" by David Palmer. In the back section it goes right through the loads and calculations that Wolfson did on the new beams. Essential reading for you. Try Amazon or if not I can scan the thing for you.

Even though you'd think the Wolfson Unit would have confidence in their structural design they still filled the outriggers of FT with water and then suspended it to check it was strong enough. (I think the beams were oversize)

Have you considered adding waterstays? They reduce the beam scantlings significantly.

Remember also to make the water deflecting fairings good and strong, even though they add a lot of weight. If you don't have them you'll have a very wet boat that slows in every wave

FT's new beams were an improvement on the problematic box alloy and bolted original beams which cracked and undid bolts - but the new setup was a serious overkill and added way to much weight to the boat ... so FT floated so deep you'd think she had filled water ballast tanks.
The difficulty is to get the correct balance, strength/weight ... and anyone can pile on the laminates to make an unbreakable beam.
Originally, FT was a fast boat (even though main hull had excessive rocker) purely because the platform was average light - but new beams and hull connections, plus quantities of gear carried aboard, changed the boat entirely; although safe, was now slow. The lighter, simpler, similar length Newick Third Turtle was a much better boat and left FT way behind.

I don't have plans for the Val but I do have plans for the Bucc 24 and the foam glass beams for the Twiggy Mk2. I understand that FT may have been too heavy but the Wolfson people thought it was okay. It is hard to find publicly available data on beams which is why you have to go back so far. I would love to get Jim Brown or someone who is retired to tell us what they used for safety factors.

So I would suggest Langdon gets onto Oldsailor and gets himself a set of plans for the Bucc 24. Reverse engineer these - they have a waterstay as Richard recommends. Cantilever tubes is a lot more load than compression with waterstay.

If you want Langdon I can either scan or redraw the Twiggy Mk2 beam plans and post them for you to peruse. They are foam/glass not alloy and therefore much harder to reverse engineer. So start with the Bucc.

"...you're right Beam Boy is a freely available program ...... Try it, you might like it, a lot of people find it very useful..."

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I do around 85% of my calculations by hand, so no need for such a program. I have also written spreadsheets of my own for 'simple' moment of inertia calc's. When the arrangement is too complex that i can't be bothered with endless "EIy" bending moment equations, i use FEA. But thanks for the suggestion.

What these programs wont tell you is it a sensilble and designed for production.

But whatever method you select, the main part is defining the load, once that is done, it is a simple job.

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